>>11937044finishing up, part 1
>>11937477>>11937516Recall the deBroglie relation for wave . Taking our quantization steps, we do the following:
and we obtain the system in my last post. I looked over this and found I had just stated this was the Hamiltonian - no, it's actually the quantized Hamiltonian. You can look at the equation of the regular one and see everything fits though. Anyway, this is the evolution of a single non-relativistic particle in 3 space over time. Recall that the Bohr model yielded, for positive integer values (this is where eigenfunctions become useful), the following energy calculation
which exactly matches with Rydberg's findings. Schrodinger used these values to test his equation for an electron moving in the potential field from the nucleus at the origin with charge e, namely
which corresponds to Hamiltonian
which has Schrodinger equation
He looked for solutions whose dependence on time was exponential. It's easier to see this when you write it
with Hamiltonian partial differentiation operator . When we search for solutions
We get exactly, when using our Schrodinger equation written in terms of the Hamiltonian operator
